Cossack Chaika Under Oars

What is modelled

A chaika is a long narrow boat driven by rowers. The crew can deliver only a limited power, and the water resists the hull in two ways: friction along the wetted surface, and the energy carried away by the waves the hull makes. The boat settles at the speed where the power the oars deliver equals drag times speed. Wind adds to or takes away from the drag.

Equations

• Displacement ∇ = M / ρ, draft T = ∇ / (Cb L B) and wetted surface S ≈ 1.7 L T + ∇ / T.
• Friction Rf = ½ ρ S Cf v² (1 + k) with Cf = 0.075 / (log10 Re − 2)².
• Wave resistance by an empirical Froude-number form Rw = ρ g ∇ · 0.8 Fn4 e−0.6/Fn², Fn = v / √(gL).
• Power balance 0.6 n Pr = R(v) v and hull speed v = √(gL / 2π) (wavelength equal to the length).

Checks run in the page

• The friction line against a second formula over three decades of Reynolds number.
• Archimedes by integrating the sections of the hull over its length.
• The residual of the power balance at the bisection root.
• The deep-water wavelength at hull speed from the wave relation.

Honest simplifications

The wave-resistance expression is an illustrative surrogate with the right trends (it rises steeply near Froude number 0.4), not a measured curve for a chaika; the form factor, block coefficient, crew mass, oar efficiency and the wind area are fixed round numbers, rowers all deliver the same average power, and the hull is not allowed to trim or squat.

• Press Light crew and Chaika, 24 rowers and compare the speeds: doubling the crew does not double the speed.
• Press Head wind 8 m/s and Tail wind 8 m/s and read the speed change in the last graph.
• Press Short and heavy and see the hull speed fall with the length.